Is Everything an Abstraction?

A question got hold of me today and I couldn’t shake it. When I try to picture what a table really is, I can’t make it stop somewhere solid.

A table is wood and grain. Wood is cells. Cells are molecules, and molecules are atoms. An atom used to be the end of the line. The name even means “uncuttable.” But it isn’t the end. It’s electrons around a nucleus. The nucleus is protons and neutrons. Those are quarks, held together by gluons. And when I push on the electron, it stops acting like a small object at all. It becomes an excitation in a field, a bump in a mathematical structure spread through space. Push further and the field turns into equations I don’t know how to picture.

Somewhere on the way down, the solid table became an idea. And I never reached a floor. There was no final layer that was obviously real, no thing that all the descriptions were describing. That absence is what tempted me toward a clean conclusion. Maybe everything is an abstraction. Maybe there’s nothing down there but our models, all the way down.

I think that conclusion is too fast. But the honest alternative turned out to be stranger than the confident realism it was supposed to replace.

Two ways to read the same success

The thing I couldn’t dismiss is that science works absurdly well. Quantum electrodynamics predicts the electron’s magnetic moment, and experiment confirms it to more than ten digits. That is not the accuracy of a lucky guess.

There is a realist way to read that success. Our best theories predict so well because they have caught hold of something real. Hilary Putnam called this the “no miracles” argument. It would be an absurd coincidence if a theory that gets the world this right were not, in some way, about the world. Electrons behave the same in a chemistry lab, a particle accelerator, and the phone in my pocket. It is hard to believe that kind of consistency is just bookkeeping.

There is also an instrumentalist way to read it. Bas van Fraassen and others treat a theory as a tool. It organizes what we observe and predicts what we haven’t seen yet. “Electron” is a name for a pattern, a very well confirmed one, and I can use the equation down to the last decimal without believing in the little ball behind it. On this view, asking whether electrons are really real is a bit like asking whether the equator is really there. We can’t do without it, and it isn’t a thing.

Here is what bothered me. The same track record supports both readings.

The evidence doesn’t decide

The realist leans on success. The instrumentalist has a sharp answer, which Larry Laudan called the pessimistic meta-induction. Look at the history. Phlogiston, caloric, the luminiferous ether. Each was the electron of its day. Central, predictive, sincerely believed. And each one is gone now. If our best past theories were wrong about what exists, even while they worked beautifully, what makes ours so different? Success has come apart from truth before.

Neither side wins, and it took me a while to see why. They are reading the same facts. The same history of theories that worked and were then thrown out. The realist sees continuity and reads it as a real target getting closer. The instrumentalist sees a graveyard of dead pictures and reads it as tools being swapped. No experiment tells them apart, because they don’t disagree about any prediction. They disagree about what the success means. And the world doesn’t settle that by running one more experiment.

What actually survives

There is a stronger realist position that takes the graveyard seriously. It’s the one I found hardest to argue with.

When a theory falls, the picture dies but the math often lives. Newton’s gravity was a force reaching instantly across empty space. Einstein replaced it with the curving of spacetime, a completely different story about what is going on. But Newton’s equations did not disappear. They come back as the low-speed, weak-field limit of Einstein’s. Fresnel had the wrong idea about light, ripples in an elastic ether, but the right equations for how it bends and reflects. Maxwell kept the equations and dropped the ether.

John Worrall calls this structural realism. What science keeps across its revolutions is structure. The relations, the symmetries, the equations. Not the intuitive stuff we drape over them. If anything is real, it is the structure.

I keep noticing how much this gives away. The electron as a tiny ball is gone, and nobody defends it. What is left to be “real” is a web of mathematical relations. That is a long way from the solid table I started with. So the strongest honest thing I can say for realism is not “the things are real.” It is “the pattern is real, and we keep the pattern even when the theory collapses.” And that sits close to the instrumentalist’s tool. Close enough that I can feel the two positions leaning toward each other. Almost everyone agrees that we track structure. The fight shrinks down to one question. Is structure all there is, or only all we can reach?

That question drags a second one behind it. Why is the part that survives always mathematical? Eugene Wigner called this the unreasonable effectiveness of mathematics. And again there are two readings. Reality is mathematical at bottom, says the realist. We keep only the math that fits and call the fit a discovery, says the instrumentalist. Same fact, two bets.

A ceiling on both

Then there is a limit that may not be one we can ever get past.

In 1936 Alan Turing proved that some perfectly clear questions have no algorithmic answer. The famous one is the halting problem. No program can decide, for every program, whether it will stop or run forever. This is not a gap that a cleverer method will close later. It is a proved boundary on what step-by-step description can do.

I was tempted to hand this straight to the metaphysics. See, reality itself escapes our descriptions. But that is an over-claim, and I want to be careful. Uncomputability is a fact about algorithms. It is not a proven fact about the universe. Going from “no algorithm decides this” to “reality is beyond us” is exactly the kind of leap this whole essay is circling. You cannot read it off Turing’s theorem. What the theorem does give me is a clean, non-mystical proof that description has an inside and an outside. That rhymes with a much older idea, Kant’s thing-in-itself. Our minds come with structure built in, and we only ever meet the world through it, never bare. Whether that structure is a window or a wall is, once again, not something we get to check from outside.

The bet

So, is everything an abstraction?

Everything we can say is. Every layer I reached was a description. Atom, electron, field, equation. Under each one was another description, and never a bare thing sitting still to be named. That much I’m confident about.

But “everything we can say is an abstraction” is not the same sentence as “everything is an abstraction.” The second one reaches past anything a description could check. It is a claim about what is there when we stop describing, made with the only tool we have, which is describing. That is the move I don’t think the evidence allows, in either direction. The realist who says the structure is really out there, and the instrumentalist who says there is only ever our models, are both standing past the edge of what any experiment could confirm. They are making bets about the limits of knowledge and reporting them as facts about the world.

Here is what I actually took from all this. It is not an answer. It is that the question has a shape, and one fact inside it won’t go away. Structure persists. Theories fall, and the equations, or the exact points where they break, climb out of the wreckage and into whatever comes next. Something is being tracked. Whether that something is the world, or just the most stable thing our minds know how to build, I don’t know. And I have come to think the not-knowing is the honest end of the road, not a sign that I need to read one more paper.

Everything we can reach is an abstraction. Whether that is a fact about us or a fact about the world is the one question our abstractions can’t reach.

References

1. Immanuel Kant, Critique of Pure Reason (1781) — the distinction between phenomena and the thing-in-itself.
2. Bas van Fraassen, The Scientific Image (1980) — constructive empiricism, a modern form of instrumentalism.
3. Hilary Putnam, Mathematics, Matter and Method (1975) — the “no miracles” argument for scientific realism.
4. Larry Laudan, “A Confutation of Convergent Realism” (1981) — the pessimistic meta-induction.
5. John Worrall, “Structural Realism: The Best of Both Worlds?” (1989) — structure as what survives theory change.
6. Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” (1960).
7. Alan Turing, “On Computable Numbers, with an Application to the Entscheidungsproblem” (1936) — uncomputable problems and the halting problem.